Block #374,914

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/25/2014, 9:19:47 AM · Difficulty 10.4190 · 6,424,025 confirmations

2CC

Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header

Block Hash

a0b0df2adae4c4da30cde10154f9a5ed2a341408fa96f9c04fb30b016c1662f7

View on Chainz ↗

Height

#374,914

Difficulty

10.418993

Transactions

Size

935 B

Version

Bits

0a6b431e

Nonce

208,854

Timestamp

1/25/2014, 9:19:47 AM

Confirmations

6,424,025

Mined by

⛏️ aRAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

605774eae4316edaa9f79a95ab81cde9fa6f068ffa23481adb1ab13ab5c6a750

Transactions (1)

Coinbase605774eae4316e…1ab13ab5c6a750

1 in → 23 out9.2000 XPM845 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.761 × 10⁹⁴(95-digit number)

17615544098291995987…16462293809881770881

Discovered Prime Numbers

p_k = 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

origin + 1

1.761 × 10⁹⁴(95-digit number)

17615544098291995987…16462293809881770881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.523 × 10⁹⁴(95-digit number)

35231088196583991975…32924587619763541761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

7.046 × 10⁹⁴(95-digit number)

70462176393167983950…65849175239527083521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.409 × 10⁹⁵(96-digit number)

14092435278633596790…31698350479054167041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.818 × 10⁹⁵(96-digit number)

28184870557267193580…63396700958108334081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.636 × 10⁹⁵(96-digit number)

56369741114534387160…26793401916216668161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.127 × 10⁹⁶(97-digit number)

11273948222906877432…53586803832433336321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.254 × 10⁹⁶(97-digit number)

22547896445813754864…07173607664866672641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.509 × 10⁹⁶(97-digit number)

45095792891627509728…14347215329733345281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

9.019 × 10⁹⁶(97-digit number)

90191585783255019456…28694430659466690561

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer